backgammon

Backgammon

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Backgammon is a board game for two players in which pieces are moved

according to the roll of dice. The winner is the first to remove all

of her own pieces from the board. Many variants have developed

throughout the world, but most share common elements. It is a member

of the tables family, one of the oldest classes of board games in the

world.

Although the game has a substantial random component, backgammon

offers a significant scope for strategy. With each roll of the dice, a

player must choose from numerous options for moving the checkers and

plan for possible counter-moves by the opponent. Opportunities for

raising the stakes of the game introduce more strategic intricacies.

Players have developed a vocabulary for common tactics and

occurrences.

Like chess, backgammon has been studied considerably by computer

scientists. Research has resulted in backgammon software that is

capable of beating world-class human players.

History

The ancient Egyptian game senet resembled backgammon, with moves

controlled by the roll of dice. The Royal Game of Ur, played in

ancient Mesopotamia, however, is a more likely ancestor of modern

tables games. Excavations at the "Burnt City" in Iran showed that a

similar game existed there around 3000 BC. The artifacts include two

dice and 60 pieces, and the set is believed to be 100 to 200 years

older than the sets found in Ur.

The ancient Romans played a number of games remarkably similar to

backgammon. Ludus duodecim scriptorum ("game of twelve lines") used a

board with three rows of 12 points each, and the pieces were moved

across all three rows according to the roll of dice. Little specific

text about the gameplay has survived. Tabula, meaning "table" or

"board", was a game mentioned in an epigram of Byzantine Emperor Zeno

(AD 476-481). It was similar to modern backgammon in that the object

of the game was to be the first to bear off all of one's checkers.

Players threw three dice and moved their checkers in opposing

directions on a board of 24 points.

In the 11th century Shahnameh, the Persian poet Ferdowsi credits

Burzoe with the invention of the tables game nard in the 6th century.

He describes an encounter between Burzoe and a Raja visiting from

India. The Raja introduces the game of chess, and Burzoe demonstrates

nard, played with dice made from ivory and teak.

The jeux de tables, predecessors of modern backgammon, first appeared

in France during the 11th century and became a favorite pastime of

gamblers. In 1254, Louis IX issued a decree prohibiting his court

officials and subjects from playing. Tables games were played in

Germany in the 12th century, and had reached Iceland by the 13th

century. The Alfonso X manuscript Libro de los juegos, completed in

1283, describes rules for a number of dice and tables games in

addition to its extensive discussion of chess. By the 17th century,

tables games had spread to Sweden. A wooden board and checkers were

recovered from the wreck of the Vasa among the belongings of the

ship's officers.

In the 16th century, Elizabethan laws and church regulations

prohibited playing tables, but by the 18th century backgammon was

popular among the English clergy. Edmund Hoyle published A Short

Treatise on the Game of Backgammon in 1743; this described rules and

strategy for the game and was bound together with a similar text on

whist.

In English, the word "backgammon" is most likely derived from "back"

and Middle English "gamen", meaning "game" or "play". The earliest use

documented by the Oxford English Dictionary was in 1650.

The most recent major development in backgammon was the addition of

the doubling cube. It was first introduced in 1926 or 1927 in New York

City among members of gaming clubs in the Lower East Side. The cube

required players not only to select the best move in a given position,

but also to estimate the probability of winning from that position,

transforming backgammon into the expected value-driven game played in

the 20th and 21st centuries.

Rules

The objective of backgammon is to move all of one's own checkers past

those of one's opponent and then remove them from the board. The

pieces are scattered at first and may be blocked or hit by the

opponent. Because the playing time for each individual game is short,

it is often played in matches, where victory is awarded to the first

player to reach a certain number of points.

Setup

Each side of the board has a track of 12 long triangles, called

points. The points are considered to be connected across one edge of

the board, forming a continuous track in the shape of a horseshoe, and

are numbered from 1 to 24. Each player begins with two checkers on her

24-point, three checkers on her 8-point, and five checkers each on her

13-point and her 6-point. The two players move their checkers in

opposing directions, each from her own 24-point toward her 1-point.

Points 1 through 6 are called the home board or inner board, and

points 7 through 12 are called the outer board. The 7-point is

referred to as the bar point, and the 13-point as the mid point.

Movement

To start the game, each player rolls one die, and the player with the

higher number moves first using the numbers shown. The players then

alternate turns, rolling two dice at the beginning of each turn.

After rolling the dice a player must, if possible, move checkers

according to the number of pips shown on each die. For example, if the

player rolls a 6 and a 3 (noted as "6-3"), she must move one checker

six points forward, and another checker three points forward. The same

checker may be moved twice as long as the two moves are distinct: six

and then three, or three and then six, but not all nine at once. If a

player rolls two of the same number, called doubles, she must play

each die twice. For example, upon rolling a 5-5 she must move four

checkers forward five spaces each.

In the course of a move, a checker may land on any point that is

unoccupied or is occupied only by a player's own checkers. It may also

land on a point occupied by exactly one opposing checker; such a lone

piece is called a blot. In this case, the blot has been hit, and is

placed in the middle of the board on the bar that divides the two

sides of the playing surface. A checker may never land on a point

occupied by two or more opposing checkers; thus, no point is ever

occupied by checkers from both players simultaneously.

Checkers placed on the bar re-enter the game through the hitting

player's home board. A roll of 2 allows the checker to enter on the

23-point, a roll of 3 on the 22-point, and so forth. A player may not

move any other checkers until all of her checkers on the bar have

re-entered the game.

When all a player's checkers are in her home board, she may start

removing them; this is called bearing off. A roll of 1 may be used to

bear off a checker from the 1-point, a 2 from the 2-point, and so on.

A die may not be used to bear off checkers from a lower-numbered point

unless there are no checkers on any higher points.

If one player has not borne off any checkers by the time her opponent

has borne off all fifteen, she has lost a gammon, which counts for

double a normal loss. If the losing player still has checkers on the

bar or in her opponent's home board, she has lost a backgammon, which

counts for triple a normal loss.

Doubling cube

To speed up match play and to provide an added dimension for strategy,

a doubling cube is normally used. The doubling cube is a six-sided die

marked with the numbers 2, 4, 8, 16, 32 and 64. Before rolling the

dice on her turn, a player may demand that the game be played for

twice the current stakes. Her opponent must either accept the new

stakes or resign the game immediately. Thereafter, the right to

redouble belongs exclusively to the player who last accepted a double.

Whenever a player accepts doubled stakes, the cube is placed with the

corresponding power of two facing upward.

The game is rarely redoubled beyond four times the original stake, but

there is no limit on the number of doubles. Although 64 is the highest

number depicted on the doubling cube, the stakes may rise to 128, 256,

and so on. In money games, a player is often permitted to "beaver"

when offered the cube, doubling the value of the game again, while

retaining possession of the cube.

The Jacoby rule allows gammons and backgammons to count for their

respective double and triple values only if the cube has already been

offered and accepted. This encourages a player with a large lead to

double, possibly ending the game, rather than to play it to conclusion

hoping for a gammon or backgammon. The Jacoby rule is widely used in

money play but is not used in match play.

The Crawford rule is designed to make match play more equitable for

the player in the lead. If a player is one point away from winning a

match, her opponent will always want to double as early as possible in

order to catch up. Whether the game is worth one point or two, the

trailing player must win to continue the match. To balance the

situation, the Crawford rule requires that when a player first reaches

a score one point short of winning, neither player may use the

doubling cube for the following game, called the Crawford game. After

the Crawford game, normal use of the doubling cube resumes. The

Crawford rule is used in tournament match play.

Variants

There are many variants of standard backgammon rules. Some are played

primarily throughout one geographic region, and others add new

tactical elements to the game. Variants commonly alter the starting

position, restrict certain moves, or assign special value to certain

dice rolls.

Acey-deucey is a variant of backgammon in which players start with no

checkers on the board, and must bear them on at the beginning of the

game. The roll of 1-2 is given special consideration, allowing the

player to select doubles of her choice. A player also receives an

extra turn after a roll of 1-2 or of doubles.

Hypergammon is a variant of backgammon in which players have only

three checkers on the board, starting with one each on the 24-, 23-

and 22-points. The game has been strongly solved, meaning that exact

equities are available for all 32 million possible positions.

Nackgammon is a variant of backgammon invented by Nack Ballard in

which players start with one less checker on the six point and

midpoint and two checkers on the 23 point.

Strategy and tactics

Backgammon has an established opening theory, although it is less

detailed than that of games like chess. The tree of checker positions

expands rapidly because of the number of possible dice rolls and the

moves available on each turn. Recent computer analysis has offered

more insight on opening plays, but the midgame is reached quickly.

After the opening, backgammon players frequently rely on some

established general strategies, combining and switching among them to

adapt to the changing conditions of a game.

The most direct strategy is simply to avoid being hit, trapped, or

held in a stand-off. A "running game" describes a strategy of moving

as quickly as possible around the board, and is most successful when a

player is already ahead in the race. When this fails, a player may opt

for a "holding game", maintaining control of a point on her opponent's

side of the board, called an anchor. As the game progresses, this

player may gain an advantage by hitting an opponent's blot from the

anchor, or by rolling large doubles that allow the checkers to escape

into a running game.

The "priming game" involves building a wall of checkers, called a

prime, covering a number of consecutive points. This obstructs

opposing checkers that are behind the prime. A checker trapped behind

a six-point prime may not escape until the prime is broken. A

particularly successful priming effort may lead to a "blitz", which is

a strategy of covering the entire home board as quickly as possible

while keeping one's opponent on the bar. Because the opponent has

difficulty re-entering from the bar or escaping, a player can quickly

gain a running advantage and win the game.

A "backgame" is a strategy of placing two or more anchors in an

opponent's home board, while building a prime in one's own board. The

anchors obstruct the opponent's checkers and create opportunities to

hit them as they move home. The backgame is generally used only to

salvage a game wherein a player is already significantly behind; using

a backgame as an initial strategy is usually unsuccessful.

"Duplication" refers to the placement of checkers such that one's

opponent needs the same dice rolls to achieve different goals. For

example, a player may position all of her blots in such a way that her

opponent must roll a 2 in order to hit any of them, reducing the

probability of being hit. "Diversification" refers to a complementary

tactic of placing one's own checkers in such a way that more numbers

are useful.

Many positions require a measurement of a player's standing in the

race, for example, in making a doubling cube decision, or in

determining whether to run home and begin bearing off. The minimum

total of dice rolls needed to move a player's checkers around and off

the board is called the "pip count". The difference between the two

players' pip counts is frequently used as a measure of the leader's

racing advantage. Players often use mental calculation techniques to

determine pip counts in live play.

Social and competitive play

Club and tournament play

Enthusiasts have formed clubs for social play of backgammon. Local

clubs may hold informal gatherings, with members meeting at caf�s and

bars in the evening to play and converse. A few clubs offer additional

services, maintaining their own facilities or offering computer

analysis of troublesome plays. Some club leaders have noticed a recent

growth of interest in backgammon, and attribute it to the game's

popularity on the internet.

A backgammon chouette permits three or more players to participate in

a single game, often for money. One player competes against a team of

all the other participants, and positions rotate after each game.

Chouette play often permits the use of multiple doubling cubes.

Backgammon clubs may also organize tournaments. Large club tournaments

sometimes draw competitors from other regions, with final matches

viewed by hundreds of spectators. The top players at regional

tournaments often compete in major national and international

championships. Winners at major tournaments may receive prizes of tens

of thousands of dollars.

International competition

Prior to 1979, there was no single world championship competition in

backgammon, although a number of major tournaments were held in Las

Vegas and the Bahamas. Since 1979, the World Backgammon Championship

in Monte Carlo has been widely acknowledged as the top international

tournament. The Monte Carlo tournament draws thousands of players and

spectators, and is played over the course of a week.

By the 21st century, the largest international tournaments had

established the basis of a tour for top professional players. Major

tournaments are held yearly in St. Tropez, Rio de Janiero, Dallas, and

Venice. PartyGaming sponsored a tournament in the Bahamas in January

2007 with a prize pool of one million dollars, the largest for any

tournament to date.

Gambling

When backgammon is played for money, the most common arrangement is to

assign a monetary value to each game, and to play to a certain score,

or until either player chooses to stop. The stakes are raised by

gammons, backgammons, and use of the doubling cube. Backgammon is

sometimes available in casinos. As with most gambling games,

successful play requires a combination of luck and skill, as a single

dice roll can sometimes significantly change the outcome of the game

Software

Play and analysis

Backgammon has been studied considerably by computer scientists.

Neural networks and other approaches have offered significant advances

to software for gameplay and analysis.

The first strong computer opponent was BKG 9.8. It was written by Hans

Berliner in the late 1970s on a DEC PDP-10 as an experiment in

evaluating board game positions. Early versions of BKG played badly

even against poor players, but Berliner noticed that its critical

mistakes were always at transitional phases in the game. He applied

principles of fuzzy logic to improve its play between phases, and by

July 1979, BKG 9.8 was strong enough to play against the ruling world

champion Luigi Villa. It won the match, 7-1, becoming the first

computer program to defeat a world champion in any board game.

Berliner stated that the victory was largely a matter of luck, as the

computer received more favorable dice rolls.

In the late 1980s, backgammon programmers found more success with an

approach based on artificial neural networks. TD-Gammon, developed by

Gerald Tesauro of IBM, was the first of these programs to play near

the expert level. Its neural network was trained using temporal

difference learning applied to data generated from self-play.

According to assessments by Bill Robertie and Kit Woolsey, TD-Gammon's

play was at or above the level of the top human players in the world.

Woolsey said of the program that "There is no question in my mind that

its positional judgment is far better than mine."

Neural network research has resulted in two modern commercial

programs, Jellyfish and Snowie, as well as the shareware BGBlitz and

the free software GNU Backgammon. These programs not only play the

game, but offer tools for analyzing games and offering detailed

comparisons of individual moves. The strength of these programs lies

in their neural networks' weights tables, which are the result of

months of training. Without them, these programs play no better than a

human novice.

Internet play

Backgammon software has been developed not only to play and analyze

games, but also to facilitate play between humans over the internet.

Dice rolls are provided by random or pseudorandom number generators.

Real-time online play began with the First Internet Backgammon Server

in 1992. It is the longest running non-commercial backgammon server

and retains an international community of backgammon players. Several

commercial websites also offer online real-time backgammon play. Yahoo

Games offers a Java-based online backgammon room, and MSN Games offers

a game based on ActiveX. Online gambling providers began to expand